Discrete schemes for Gaussian curvature and their convergence
Computer Vision and Pattern Recognition
2008-04-09 v1 Computational Geometry
Graphics
Numerical Analysis
Abstract
In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over the regular vertex with valence 4. Finally, asymptotic errors of several discrete scheme for Gaussian curvature are compared.
Keywords
Cite
@article{arxiv.0804.1046,
title = {Discrete schemes for Gaussian curvature and their convergence},
author = {Zhiqiang Xu and Guoliang Xu},
journal= {arXiv preprint arXiv:0804.1046},
year = {2008}
}